## Description

The purpose of this study was to determine how well children in grade 1 through 6 understand the concepts of common fractions by (1) interviewing a selected group of pupils from these grades, (2) administering a comparable written test to one class at each grade level, and (3) comparing the results of the interview with the results of the written test. Sixty children, ten from each grade, 1 through 6, were selected for the interview on the bases of an intelligence quotient in the range from 95-105; and no child who had failed in any grade was accepted for this experiment. The questions in the interview were designed to test the concepts of common fractions. For the purpose of comparison, a written test based on the interview questions was constructed. The order of the items for the written test and the interview were identical and corresponded to their grade placement in the California State Textbooks in Arithmetic. The written test was administered to one entire class at each grade level. The classes that were given the written test were selected on two criteria; a single grade per room, and the room in which the interviewees were class members. The results of the interview, written test, and the comparisons were computed and tabulated. The results of the interview and the written test showed that the interview group had a higher mean percent of correct responses than the written test group. The interview group for grades 1 through 4 had a higher mean percent of correct responses than the written-test group, while the written-test group for grades 5 and 6 had a greater mean percent of correct answers than the interview group. The growth curves for both groups were similar with the greatest periods of growth occurring between first and second grade, and third and fourth grade. Several specific conclusions based on the evidence obtained by this study were made. 1. Dividing a whole into halves or fourths is understood at all grade levels. 2. The definitions that pupils possess for terms commonly used in working with the fractions are inadequate. 3. Writing fractions is difficult for pupils in grades 1 through 4. 4. The concept that when several fractions have the same numerator, the fraction with the largest (or smallest) denominator is the smallest (or largest) fraction is not fully understood at any grade level. 5. The concept that multiplying and dividing both terms of a fraction by the same number does not change its value is not fully understood at any grade level. In general, pupils in grades 1 through 5 possess inadequate understanding of the meanings of common fractions. Pupils have a tendency to apply incomplete concepts when working with common fractions. When confronted with unfamiliar situations, few pupils use reasoning to solve the problems.